Title: A mathematical model for locating k-obnoxious facilities on a plane

Authors: U.K. Bhattacharya

Addresses: Indian Institute of Management Indore, Rau, Pigdamber, Indore, Madhya Pradesh, 453556, India

Abstract: This paper proposes a new mathematical model for locating k-obnoxious facilities Here a vertex covering k-obnoxious facilities location problem on a plane has been modelled by combining it as a combination of three interacting criteria as follows: 1) maximise the minimum distances between any existing point and any variable point as well as between any pair of variable points; 2) maximise the number of existing points covered by various respective variable points; 3) minimise the overall importance of the various existing points associated to the various variable facility points. A nonlinear programming iterative algorithm for locating k-obnoxious facilities has been developed. The algorithm developed here is a generalised iterative algorithm. It has been proved that the optimal solution obtained by the algorithm is the non-dominated solution of the original multi-objective problem. Rectilinear distance norm has been considered as the distance measure as it is more appropriate to the various realistic situations.

Keywords: multiple-criteria analysis; obnoxious facility location; utility approach; non-dominated solution.

DOI: 10.1504/IJOR.2018.089738

International Journal of Operational Research, 2018 Vol.31 No.3, pp.384 - 402

Received: 02 Apr 2015
Accepted: 22 May 2015
Published online: 09 Feb 2018 *

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